Solve for $x$ and $y$ using elimination. ${-2x-3y = -28}$ ${5x-4y = -22}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $2$ ${-10x-15y = -140}$ $10x-8y = -44$ Add the top and bottom equations together. $-23y = -184$ $\dfrac{-23y}{{-23}} = \dfrac{-184}{{-23}}$ ${y = 8}$ Now that you know ${y = 8}$ , plug it back into $\thinspace {-2x-3y = -28}\thinspace$ to find $x$ ${-2x - 3}{(8)}{= -28}$ $-2x-24 = -28$ $-2x-24{+24} = -28{+24}$ $-2x = -4$ $\dfrac{-2x}{{-2}} = \dfrac{-4}{{-2}}$ ${x = 2}$ You can also plug ${y = 8}$ into $\thinspace {5x-4y = -22}\thinspace$ and get the same answer for $x$ : ${5x - 4}{(8)}{= -22}$ ${x = 2}$